Question

Graph. Find an ordered pair and where they intersect.y=-1/4x+2y=1/2x-1

Answer 1

We need to solve the following equation system:

`\begin{gathered} y=-(1)/(4)x+2 \\ y=(1)/(2)x-1 \end{gathered}`

We can do this by graphing both equations and find the point where they intersect. To graph them, we need two points that belong to each equation.

For equation 1, we have:

`y=-(1)/(4)\cdot0+2=2`

Which means our first point is (0, 2).

`\begin{gathered} 0=-(1)/(4)\cdot x+2 \\ -(1)/(4)\cdot x=-2 \\ x=-2\cdot(-4) \\ x=8 \end{gathered}`

The second point is (8,0).

For equation 2, we have:

`y=(1)/(2)\cdot0-1=-1`

So the first point is (0, -1).

`\begin{gathered} 0=(1)/(2)\cdot x-1 \\ (1)/(2)\cdot x=1 \\ x=2 \end{gathered}`

So the second point is (2, 0).

Now we can graph both equations.

We need to find the point at which they intersect each other. We can see that they intersect right above x = 4, if we look at the y-axis, the height is approximately y=1. So the point of intersection is (4, 1).